During a competitive period when well-reviewed wide releases like “Dunkirk” and “Baby Driver” are luring adult audiences away from new smart-house fare, Weinstein stormed back at the specialty box office with Taylor Sheridan’s Wyoming western “Wind River,” which boasted one of the best limited openings of the year. A strong debut will help it stand out in the weeks ahead as the flow of new films declines.

Fox Searchlight welcomed a decent initial response for its heart-tugging inner-city dance documentary “Step” in seven cities. Also impressive is the two-theater launch for “Columbus,” starring Jon Cho as a Korean translator spending time in middle America due to a family emergency.

Opening

Taylor Sheridan’s well-received rural thriller debuted with the strongest limited debut since late June’s “The Big Sick” and “The Beguiled.” Since then an array of festival successes with similarly upbeat reviews have opened. It’s The Weinstein Company’s best limited opening since “Carol” in late 2015 (better than “Lion,” which went on with an Oscar boost to over $50 million), so this is a return to form for the once-dominant player in the specialized world. Saturday increased a healthy 23 per cent from Friday, suggesting good initial audience response.

What comes next:This expands to the top 20 markets this Friday, with likely extensive wider play beyond.

Per usual, Fox Searchlight opened this documentary focused on a step-dancing team at an inner-city girls school in Baltimore in more than the standard two coastal cities. Its seven-market start in varied specialized and mainstream theaters will serve as a launch for its rapid expansion to 125 or more theaters this Friday.

Word of mouth is key, so the Sundance hit has been seen by a sufficient number of viewers to give it a shot at broader play. On the other hand, Saturday’s numbers stayed even with Friday, better than some studio releases but not as strong as many limited releases. (Searchlight’s recent “Gifted” opened in nearly double the theater count in April and increased 35 per cent on its second day.)

What comes next: The second week expansion is the start of a much wider planned national release.

Rave reviews helped the two-theater New York/Los Angeles initial release for this Sundance Next section premiere. John Cho plays an estranged son who rushes to Columbus, Indiana (a center of modern architecture) when his father collapses. While his encounters there with a young tour guide make an unlikely basis for a contemporary specialized American movie, this debut feature has struck a chord. This could be sleeper success with continued careful handling (it is self-distributed).

What comes next: Seattle and San Francisco are next this Friday with top markets set over the upcoming weeks.

We Love You Sally Carmichael! (Purdie)

$(est.) 28,000 in 7 theaters; PTA: $(est.) 4,000

This home-grown Utah family story is about an anonymous popular romance novelist whose true identity is discovered, to his horror. It played top Salt Lake City and other area theaters to a passable initial response.

What comes next: This will likely get additional local attention for starters.

Week Two

An Inconvenient Sequel: Truth to Power (Paramount)

$900,000 in 180 theaters (+170); PTA: $5,000; Cumulative: $1,052,000

Paramount is lending major support to this climate change activist documentary sequel, with credible if not spectacular results. The second weekend for the original grossed (adjusted) an average of almost $25,000 in 77 theaters. This looks headed for a result that will place it both among the top-grossing documentary titles of the year but far below the “An Inconvenient Truth” total in 2006.

Menashe (A24)

$80,317 in 10 theaters (+7); PTA: $8,032; Cumulative: $178,834

Among the few foreign-language films finding success these days, a handful about Orthodox communities in Israeli have stood out. Now a domestic New York custody story set in an ultra-orthodox community where observance controls all aspects of life is showing some initial success in its second weekend as it slowly expands.

“Brigsby Bear”

Courtesy of Sundance

The Brigsby Bear (Sony Pictures Classics)

$42,790 in 15 theaters (+12); PTA: $2,853; Cumulative: $97,377

A mediocre second weekend limited expansion for this quirky independent story about the impact on one young man whose life changes when his favorite kids’ TV show is cancelled.

Ongoing/expanding (Grosses over $50,000 in under 1,000 theaters)

Maudie (Sony Pictures Classics) Week 17

$262,496 in 187 theaters (-41); Cumulative: $5,148,000

This Canadian/Irish coproduction has dropped from its widest point, with the U.S. component of its combined gross reaching a decent $2.4 million so far.

“Landline”

Landline (Magnolia) Week 3

$240,000 in 131 theaters (+93); Cumulative: $503,128

Amazon’s Sundance independent drama about a Manhattan family confronted with domestic turmoil broadened to most major cities in its third weekend. It shows a mixed response at best, similar to several other well-received films that have faced competition from multiple other sources (both studio and independent) aimed at review-oriented audiences.

Lady Macbeth (Roadside Attractions) Week 4

$164,245 in 131 theaters (+27); Cumulative: $736,877

Another quality specialized drama this summer that has struggled to find its audience amid major competition.

A Ghost Story (A24) Week 5

$146,232 in 208 theaters (-181); Cumulative: $1,317,000

David Lowery’s artful return to independent film after his Disney detour with “Pete’s Dragon” had Casey Affleck and Rooney Mara in tow. But the admittedly strange film never caught on after its initial decent launch, and a little more than a month after opening, it’s down to virtually no business with a per theater average of only around $700.

“The Midwife”

The Midwife (Music Box) Week 3

$82,698 in 43 theaters (+15); Cumulative: $225,548

Music Box continues its commitment to French among other subtitled movies with this Catherine Deneuve vehicle. The drama expanded wider in its third weekend to marginal results, with further markets planned for next weekend and beyond.

The Little Hours (Gunpowder & Sky) Week 6

$75,260 in 60 theaters (-36); Cumulative: $1,348,000

A Decameron-based story about nuns and their fun is another recent decent opener that hasn’t blossomed in wider dates.

The Beguiled (Focus) Week 7

$54,495 in 89 theaters (-55); Cumulative: $10,451,000

Sofia Coppola’s Civil War drama is wrapping up its run with a respectable total.